High School Guide: Admissions, reviews, and advice
in Students & Teens ·
Terry Martinez10 said:But really, who is supposed to remember what, exactly?
The Hessian normal form is just standard material covered back in 11th or 12th grade high school... I just assumed it was part of the curriculum here too, so I didn't bother looking it up because I simply took it for granted.
Besides, how does any of this even relate to the point I was making about my enrollment?
There was mention of how some schools don't even get around to covering integrals, so I just figured if they're skipping those, there's probably a whole laundry list of other things left untouched or unmastered in the classroom.
And what does that have to do with anything you're saying?
You could swap out "Hessian normal form" for pretty much any other topic taught in an American high school and the logic remains identical: if vocational schools clearly aren't covering certain topics—which seems obvious based on various forum posts regarding enrollment—then there is undoubtedly more missing, which ultimately leads to poor preparation for college.
I certainly can't be expected to know the entire contents of every single high school curriculum in advance, regardless of the subject.
Limits, derivatives, and integrals are the very last things covered in the senior year of high school (for any track with four years of math). Integrals are literally the final unit in the curriculum; if those aren't covered, it doesn't necessarily mean nothing else was missed later on.
Why all that isn't finished, I honestly haven't a clue. I went to a specialized math prep school, so we had extra hours and we got through all of it. But kids in general education tracks have fewer hours, so maybe teachers just focus on other things and end up skipping the rest.
But, speaking as someone with quite a bit of experience with university-level math, whether those specific topics were covered in high school isn't actually that critical for college math. At almost any university, if you're studying integrals (at least nowadays), you basically start from scratch and learn them from the ground up.
And that isn't because of "poor high school preparation." It's more because university mathematics (for the 90% of people who weren't math competition kids) represents a shift toward a completely different way of thinking, specifically regarding proofs. That's where most people struggle. The problems are harder, they require more work, and they demand a deeper level of understanding—you really have to grasp the definitions and the proofs themselves.
And that's not just an issue in the former America; it's everywhere. In the US, you have the famous Calculus, which covers the basics of derivatives and integrals, mostly at a computational level (we even did some integral definitions via limits back in high school). Then you have Mathematical Analysis, which is the true mathematical approach to it. In our universities, we jump straight into Mathematical Analysis.
Personally, I think your approach of using "random topic X" is just silly. First off, when I looked up what that was, I couldn't see any connection to college prep. Something you can read a definition for in ten seconds and immediately understand shouldn't be considered a major pillar of college readiness.
